frequency domain based ls channel estimation in ofdm based

Mario Bogdanovic

Frequency domain based LS channel estimation in OFDM basedPower line communications

DOIUDKIFAC

10.7305/automatika.2014.12.639621.391.3:621.315.027.22.1.5; 5.8

Original scientific paper

This paper is focused on low voltage power line communication (PLC) realization with an emphasis on channelestimation techniques. The Orthogonal Frequency Division Multiplexing (OFDM) scheme is preferred technologyin PLC systems because of its effective combat with frequency selective fading properties of PLC channel. As thechannel estimation is one of the crucial problems in OFDM based PLC system because of a problematic area ofPLC signal attenuation and interference, the improved LS estimation technique is proposed. We investigate andevaluate proposed frequency domain LS channel estimation method forOFDM based power line communicationsystem. Also performance comparing with existing pilot based estimation algorithms towards proposed method interms of their computational complexity, error correction, and suitability conditions is made.

Key words: Power Line Communication, OFDM, Channel Estimation, Least Squares estimation, Linear Mini-mum Mean-square Error estimation

LS estimacija kanala u frekvencijskoj domeni u OFDM baziranim komunikacijama preko strujnihvodova. Ovaj rad je fokusiran na realizaciju komunikacije preko vodova niskonaponske mreže s naglaskom natehnike procjene prijenosnog kanala. OFDM schema je preferirana prijenosna tehnologija u PLC sustavima zbogsvoje ucinkovitosti u borbi s osobinom selektivnog frekvencijskog išcezavanja signala kod PLC kanala. Kako jeprocjena kanala jedan od najvažnijih problema u OFDM baziranom PLC sustavu zbog problematicnog podrucjagušenja i interferencije PLC signala, predstavljena je poboljšana tehnika LS procjene kanala. Istražili smo teevaluirali predstavljenu metodu LS procjene kanala u frekvencijskoj domeni za PLC sustave bazirane na OFDMmodulacijskoj tehnici. Takoder je napravljena usporedba karakteristika predložene metode s poznatim algoritmimaprocjene kanala uz pomoc znanih simbola (pilota) u podrucju njihove racunalne složenosti, ispravljanja grešaka teuvjetima prilagodavanja.

Klju cne rijeci: komunikacija strujnim vodovima, OFDM, procjena prijenosnog kanala, procjena metodom naj-manjih kvadrata, procjena metodom linearne srednje kvadratne pogreške

1 INTRODUCTION

The electric power supply network infrastructure iscovering most parts of the inhabited areas. The grow-ing telecommunication market provides the possibility ofusing electric power system for a possible pay out mar-ket solution for advanced information technology suchas high speed data transmission, real-time video, voiceconnections, and High-definition television (HDTV). ThePLC technology has advantages in accessibility and theexisting infrastructure. On the other hand, the powerline medium was not designed for high frequency datatransmission. Frequency-dependent attenuation, changingimpedance, fading and noise conditions varying in timeare the negative properties of the PLC transmission chan-nel. So, it is important to select adequately the modulation

technique to achieve high speed data transmission in PLCchannel.

Frequency selectivity of PLC channel is caused by mul-tipath propagation, due to different impedances of termi-nations of power line [1, 2]. The OFDM has been receiv-ing growing interest in recent years due to effective com-bat with frequency selective PLC channels. The majorityof the researches in the literature recommend OFDM as arelevant solution because of its excellent bandwidth effi-ciency needed for high speed data transmission. OFDM ismulti-carrier based system and it is originated on proratedtransmission bandwidth into parallel sub-channels with or-thogonal carriers, which is an adequate solution in the caseof inter-symbol interference (ISI), signal fading, channelnoise, etc.

Online ISSN 1848-3380, Print ISSN 0005-1144ATKAFF 55(4), 487–494(2014)

487 AUTOMATIKA 55(2014) 4, 487–494

Frequency domain based LS channel estimation in OFDM based Power line communications Mario Bogdanovic

Further, channel estimation plays important role inOFDM systems and it can be used for enhancement of thesystem performance in terms of bit error rate (BER) [3,4].For the purpose of estimation, insertion of known symbolsor pilots in the OFDM signal is required and thereby chan-nel frequency response can be estimated. The most usedalgorithms for channel estimation are based on the leastsquares (LS) supported by linear and cubic interpolationand the linear minimum mean-square error (LMMSE) ap-proaches.

The rest of the paper is organized as follows. In Section2, proposed model based on coded OFDM is presented.The proposed power line channel model and environmen-tal noise are presented in Section 3. In Section 4, the basiccomb-type LS and block-type LMMSE channel estimationalgorithms is reviewed. The proposed comb-type LS esti-mation algorithm with its computational complexity is car-ried out in Section 5. Simulation results are presented anddiscussed in Section 6. The paper finishes with discussionand the conclusion in Section 7.

2 OFDM BASED PLC SYSTEM MODEL

Multi-carrier transmission techniques are based on theidea of dividing the overall bandwidth into many sub-channels with its own assigned carrier. With this solutionit can be obtained almost ideal propagation properties forall data flows even if the overall channel is characterizedby coloured noise and frequency selectivity. OFDM tech-nique can be considered as an evolution of multi-carriertechniques: it is characterized by very high spectral effi-ciency thanks to orthogonal sub-carriers utilization; sub-carriers orthogonality condition is guaranteed if frequencyspacing is equal to inverse of OFDM symbol duration. Theorthogonality guaranties that streams do not interfere withone another and multi-channel transmission provide elim-ination of inter-symbol interference (ISI) and inter-carrierinterference (ICI) phenomena.

Figure 1. PLC OFDM model

OFDM modulation splits a high data stream into anumber of lower rate streams and those streams are trans-

mitted in parallel with lower bandwidth over a numberof orthogonal sub-carriers which are distributed in a fre-quency spectrum. The selection of relevant number of sub-carriers ensures to have low-rate parallel data streams ineach sub-channel such that all of them will be ISI free. Toavoid ISI almost completely, a guard time interval needsto be added to each OFDM symbol. The guard time inter-val needs to be longer than the delay spread of the over-all channel. Also, in the guard time, the OFDM symbolshould be cyclically extended in order to avoid ICI.

Basic principle of coded OFDM with pilot channel es-timation is following (Fig. 1). The high-speed binary data,at first step at the transmitter side, has been coded and in-terleaved. Afterwards, data is distributed in several par-allel channels and mapped into adequate multi-amplitude-multi-phase signals. The next step is insertion of knownsymbols (pilots) on the predetermined position in order toperform correct channel estimation. Further, transforma-tion of modulated dataXk from frequency into time do-main data is done by IFFT [5] using IDFT (Inverse Dis-crete Fourier Transform):

xt(n) =1

N

N/2∑

k=−N/2+1

Xk ·ej2πnk/N , n = −Ng, ..., N−1 (1)

whereN is the number of total sub-carriers andxt(n) istime-domain sample. At the end of the transmitter side,protective guard interval and cyclic prefix are added. Suchcreated OFDM signal is sent over PLC multipath fadingchannel. At the receiver side, the propagated signal isgiven as:

y(n) = xt(n)⊗ h(n) + w(n) (2)

whereh(n) is the power line channel impulse response,w(n) is noise and⊗ stands for convolution operator. Af-ter the cyclic prefix is removed, received signal is sent tothe FFT block to de-multiplex using DFT (Discrete FourierTransform):

Y (k) =1

N

N−1∑

n=0

y(n)e−j2πkn/N , k = 0, 1, 2, ..., N − 1 (3)

The pilotsHp(k) are extracted from the de-multiplexed sig-nal in order to obtain the channel transfer functionH(k).The transfer functionH(k) is further used for recovering ofthe distorted transmitted data.

X(k) =Y (k)

H(k), k = 0, 1, 2, ..., N − 1 (4)

De-mapping of recovered OFDM signal into the adequateOFDM sub-channel is carried out. The two last operationsare de-interleaving and decoding, realized in order to get,as much as possible error free, reconstructed source binaryinformation at the receiver side.

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3 POWER LINE CHANNEL CHARACTERISTICS

Creating suitable channel model is essential parameterfor modeling any communication system. In the literaturedifferent power line channel models can be found. Severalapproaches are emphasizing as widely spread and ratherdeveloped so the focus is put on those two, further stated.The first one is based on methods for radio channel mod-eling and the power line channel is categorized as a mul-tipath propagation environment [1]. The above mentionedmethod is applied as the mathematical description and thesimulation model of power line channel. Second one isbased on methods used to model long electricity distribu-tion networks. This method models transfer function ofpower line channel using chain matrix theory (ABCD ma-trix theory) [6].

3.1 Multipath Signal Propagation Model

The power line medium is time varying and unstabletransmission medium. It is considerably dependent on net-work topology, cable branches and impedance mismatch.Because of those physical properties, a multipath scenariowith frequency selective fading is considered. Mathemati-cal model of transfer function (known asZimmerman andDostert model) can be defined as [2,7]:

H(f) =

N∑

i=1

|gi(f)| eϕgi(f)

︸︷︷︸weightingfactor

· e−(a0+a1fk)di

︸︷︷︸attenuationportion

· e−j2πfτi︸︷︷︸delayportion

(5)

Equation (5) describes signal propagation with the low-pass characteristic and the delay portion. Each path ischaracterized by a weighting factorgi which is the sumof transmission and reflection factors with path lengthdi.The attenuation factor is modelled by the parametersa0,a1 andk obtained from measurements.

3.2 The generalized background noise

The important factor in the PLC model is environmen-tal noise which can be categorized in following [7]:

1. coloured background noise

2. narrowband noise

3. periodic impulsive noise

4. non-periodic impulsive noise

In this work focus is put on generalized backgroundnoise WGBN which is a superposition of the colouredbackground and narrowband noise (6). Those two noisesare caused by a superposition of multiple sources of noise

Figure 2. Frequency response of power line channel (pa-rameters defined in [7])

with low power and broadcasting in short, middle and longwave ranges, respectively [8]. Given results obtained frommeasurements in the office building in Osijek city centerare statistically processed. The final result is a probabilitydensity function (PDF) for the noise power. It shows thatmeasured data fits in between exponential and Rayleighdistribution [9]. Thus, such given statistical model is fur-ther used to create appropriateWGBN model as a part ofcomplete PLC simulation system.

WGBN (f) = WCBN (f) +WNB(f)

WCBN (f) = W∞ +W0 · e−ff0

WNB(f) =∑N

i=1 Ai(t) sin(2πfit+ ϕ)

(6)

Figure 3. Measured PLC generalized background noise(0-20 MHz)

4 PILOT BASED CHANNEL ESTIMATION ALGO-RITHMS

Channel estimation has a great importance in powerline communication system. As the PLC transmissionchannel is very hostile environment for data transmission,transmitted information suffers from amplitude scaling and

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phase rotation. Channel estimation can be obtained withhelp of inserted pilots into the OFDM symbols. Thereare two wide spread methods of inserting pilots into thesignal [10]. First one dedicates entire OFDM symbol tocarry pilot samples on the all the sub-carriers for channelestimation. This kind of pilot arrangement is called theblock-type and it is suitable for slow-fading channels. Pi-lots are sent periodically in the time domain. As the train-ing block contains all frequencies, channel interpolationisnot required. Comb-type pilot arrangement is the secondmethod of pilot insertion. In comb-type method pilot sym-bols are uniformly spread on selected sub-carriers in eachOFDM block and repeated over multiple symbols. Chan-nel estimation is performed at each symbol and interpola-tion is required to infer the channel frequency values of thenon-pilot sub-carriers.

Figure 4. Block-type and Comb-type pilot arrangements

4.1 Comb-type LS Channel estimation

The relationship between transmitted signalsXk and re-ceived signalYk can be defined as:

Y i(k) = HkXik +Wk, k ∈ (0,M − 1) (7)

whereY is the vector containing received pilots,X is avector of original data from transmitter,H is a matrix ofchannel response of pilot sub-carriers andW is the vec-tor of environmental noise. Using known transmitted pilotsymbols (Xp) and received symbols (Yp) at predefined pi-lot sub-carriers, the raw channel estimate (HLS) at pilotsub-carriers can be calculated as:

HLS =Yp

Xp(8)

In order to estimate channel over all sub-carriers usingchannel information at the pilot-sub-carriers, the channelinterpolation is needed. The following interpolation meth-ods can be applied:

1. Linear Interpolation

2. Spline Interpolation

3. Cubic Interpolation

4. Low pass Interpolation

Phase errors caused by frame synchronization havehigh impact on channel estimation, particularly on interpo-lation methods. This error comes from a group delay of thereceived OFDM signal before de-multiplexing and conse-quently causes higher distortion at the estimated channel incomb-type systems. A simplified method of phase recov-ery can be applied to linear and polynomial interpolatorsand the change in phaseϕp can be expressed as [11]:

ϕp = ∠ 1

Nc − 1

Np−2∑

m=0

H∗LS(m)HLS(m+ 1) (9)

whereNc andNp are total number and number of pilot sub-carries, respectively. The pre-compensation of the LS esti-mation can be performed as

HLS,pe(m) = HLS(m) exp(jϕpm) (10)

wherepedenotes phase estimation.

4.2 Block-type LMMSE channel estimation

This method of channel estimation uses second orderstatistic of the channel conditions to minimize mean squareerror. Relation between transmitted signalXk and receivedsignalYk is already stated in (7). LS estimator can be de-rived from the minimization of the square error of lineardata model:

∥∥ε2∥∥ = (Y −XH)(Y −XH)

H

(11)

where superscriptH stands for Hermitian transpose. Thegradient is defined and equals zero:

∂∂H ε2 = 2XHY − 2XHXH = 0

HLS = (XXH)−1XHY

HLS = X−1Y

(12)

Minimum Mean Square Error (MMSE) channel esti-mation has an excellent performance in suppression ofnoise and ICI, but it requires the high complexity of hard-ware implementation and information about channel andnoise power level is needed [4]. Let us denote the error ofchannel estimationeas:

e = H −∧H (13)

whereH is actual channel estimation and∧H is raw channel

estimation, respectively. Minimum square error of channelis defined as:

E{|e|2

}= E

{∣∣∣∣H −∧H

∣∣∣∣2}

= E

{(H −

∧H)(H −

∧H)H

} (14)

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whereE{} is the expectation. We can rewrite (14) as:

HMMSE = RHY R−1Y Y Y (15)

whereRHH andRY Y are the auto-covariance matrixes ofH and Y, respectively. The cross covariance matrix be-tweenH andY is defined asRHY . Due to high complexityof MMSE estimation, Linear MMSE (LMMSE) channelestimator is widely used in communications [12, 13]. Us-ing Singular Value Decomposition (SVD) is the core prin-ciple to find optimum low-level LMMSE estimator. TheLMMSE estimation of channel response withσ2

W as vari-ance ofW(k)can be described as:

HLMMSE = RHH(RHH+σ2W (XHX)−1)−1HLS (16)

As the defined channel estimator need to get matrix inver-sion every time the training data inX changes. There-fore we reduce the complexity by replace the(XHX)−1

by its expectationE{(XHX)−1

}, which means the av-

erage power of all sub-carriers replace the instantaneouspower of each sub-carrier in order to reduce the compu-tation. Now the LMMSE channel estimator can be repre-sented as [13]:

HLMMSE = RHH(RHH +β

SNRI)−1HLS (17)

whereβ is constant depending on the type of modulation,SNRis signal-to-noise ratio andI is the identity matrix. Forexample, when 64 QAM is used theβ is 2.6854. After theestimation is performed and interpolated (in LS case), thephase should be restored (10) by multiplying the output byexp(−jϕpm).

5 PROPOSED PLC CHANNEL ESTIMATION

LS estimator is the simplest estimator whose perfor-mance is quite general and LMMSE is more complex andit has been successfully applied in wireless communica-tions. As the PLC channel has different properties fromradio environment, the environmental noise and channelcharacteristics is time-variant through the day, a useful andsimple channel estimation algorithm is important. The de-rived LMMSE estimator requires knowledge of the chan-nel frequency correlation and the presentSNR. In the caseof fixed SNRandRHH , the matrix inversion (17) can becalculated only once reducing complexity. This methodcauses significantly degradation of the estimator perfor-mance [10, 14] because of PLC channelSNRand RHH

are unknown in advance and time varying. Hence, thematrix inversion should be calculated for each estimationOFDM block and therefore increases estimator complex-ity and processing time. The proposed LS estimator is notbased on statistical properties of the channel which reducesestimation complexity.

As we mentioned the comb-type LS estimate of transferfunctionH is susceptible to noise. Because the interpola-tion of channel is needed, we impose additional errors inchannel transfer function. On the other side, block-type es-timation gives whole channel transfer function at the givenmoment, but it needs all sub-carriers.

Figure 5. Proposed pilot arrangement

The main idea of proposed LS channel estimation al-gorithm is to combine features from comb-type and block-type channel estimation to get simple and effective estima-tor. The selected features should be suitable for combatwith specific, especially time varying, PLC channel prop-erties (Fig. 5). With the help of block-type estimation, thewhole channel and noise condition at the desired OFDMsymbol can be determined. It is performed by sending allpilot sub-carriers as the training sequence at first OFDMsymbol (and further everyLB-th symbol). On this way thehelp transfer function is generated and the result of thusobtained channel transfer functionHBT will be stored inthe receiver buffer. To avoid possibly storing a stronglydistorted transfer function as a possible result of a noise ef-fect, each following help function is adding to storedHBT

and the average value is stored into the buffer. After cer-tain time interval buffer should contain the average channelcondition for further utilizing.

After training sequence conventional comb-type LS es-timator with interpolation is used (either spline cubic orlinear) according to (8) and the result isHCT transfer func-tion that contours current state of the channel, especiallynoise condition. The proposed solution uses simple meanvalue between above defined two transfer functions to im-prove the storedHBT by momentary obtainedHCT :

HRES(k) =HBT + HCT (k)

2, k = 1, 2, ...,M (18)

whereM represents a number of useful sub-carriers (DC,data, and pilot sub-carriers).

Concerning the increase of computational complexityof the proposed algorithm against conventional LS estima-tion, the complexity is increasing with two additional av-eraging of given transfer functions -HBT on everyLB-th

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Figure 6. Theoretical channel transfer function atSNR=30dB

Figure 7. Proposed LS estimated channel transfer functionat SNR=30dB

andHRES on every symbol. Also hardware requirementsat the receiver side rise as one additionalM sized buffer isneeded.

The bandwidth efficiencyη of proposed LS estimationalgorithm can be defined as number of pilot and numberof data sub-carriers ratio in one estimation block (19). TheLB is the number of OFDM symbols,Lpilots is the numberof pilots,Lsc is the number of sub-carriers andLdata is thenumber of useful data in one estimation block (Fig. 5).The estimation block is defined as a group of one trainingsequence andLB -1 conventional LS OFDM symbols.

η =Lsc + [Lpilots · (LB − 1)]

Ldata(LB − 1)(19)

As the proposed algorithm consumes additional bandwidthfor channel estimation, the optimal size of one estimationblock is needed to minimize the loss in total transmissioncapacity and to achieve the bandwidth efficiency of con-ventional LS estimator.

6 SIMULATION RESULTS

The simulation goal is to compare functional depen-dence ofBER(bit error rate) towardsSNR(Signal to NoiseRatio) for conventional comb-type LS estimator, block-type LMMSE, and proposed LS estimation algorithm. Theinfluence of different channel characteristics (e.g., differ-ent channel topology, influence of environmental noise)on the proposed LS algorithm is investigated and per-formed. Also the bandwidth efficiency of proposed LSestimation algorithm against the conventional comb-typeLS estimator is carried out. The introduced channel esti-mation method is evaluated using a framed-based Matlaband Simulink (ver.7.9.0) simulation with the total trans-mission bandwidth up to 30 MHz. The testing scenario ofOFDM system model with 63 data and 15 pilot sub-carriersis applied. The transmission bandwidth is divided into 128sub-channels by using 128 FFT. The size of one estima-tion blockLB is set on 350 OFDM symbols. Modulationis performed with 64 QAM modulation technique. Cyclicprefix length is 1/8 of the FFT length. The PLC channel ismodelled asZimmerman and Dostertmodel with variouschannel characteristics as depicted on Fig. 2. The channelis implemented as a digital filter and attenuates the inputsignal according to a transfer function. The filter coeffi-cients are obtained from the transfer function (5) in therange from 0 to 30 MHz. The addition of environmentalnoise in the form of generalized background noise (Fig. 3)to attenuated input signal is performed.

Figure 8. Proposed LS estimator for various channeltopology (channel parameters defined in [7])

In first simulation set, the proposed LS estimation tech-nique in various channel conditions defined through sev-eral channel topologies and additional environmental noiseis performed. Simulation results depicted on Fig. 8 showsthat proposed LS channel estimator performance stronglydepends on channel condition and topology.

Further, the carried out simulation introduce perfor-mance of proposed LS estimator against conventional

AUTOMATIKA 55(2014) 4, 487–494 492


comb-type LS and block-type LMMSE channel estimatorsfor the same set of the channel topologies. Comb-type esti-mators use linear interpolation, because foregoing researcharticles reference better performance linear over spline cu-bic interpolation.

Figure 9. Comparison of conventional LS and proposed LSchannel estimation for channel model class 150 medium(Fig. 2)

Figure 10. Comparison of conventional LS and proposedLS channel estimation for channel model class 150 bad(Fig. 2)

Figure 9, Fig. 10, and Fig. 11 show better per-formance of the proposed LS estimator against conven-tional LS estimator for all three cases of different channelproperties. The enhancement of the proposed LS estima-tor against regular comb-type LS estimator rises propor-tional as the number and length of branches in channel de-creases and the channel became less frequency-selective.At SNR=30dB the improvement ofBERis 10−0.5 for badchannel properties and10−1.5 for good channel proper-ties. Moreover, for relatively simple channel complex-ity the performance of proposed LS estimator is good asLMMSE channel estimator performance (Fig. 11). Alsoin this case error free data transmission through PLC chan-

Figure 11. Comparison of conventional LS, proposed LS,and LMMSE channel estimation for channel model class150 good (Fig. 2)

nel at SNR≥30dB can be achieved. The possible usageof proposed estimator is in PLC LAN systems forin-homeor small officenetworking, where the internal electrical in-frastructure is not as complicated as inlast-milesolutionsand can exist as an independent network.

Figure 12. The bandwidth efficiency of proposed LS esti-mation algorithm

The bandwidth efficiency is investigated in correlationwith the size of estimation block (Fig. 12). For the simu-lation properties the efficiency of conventional comb-typeLS estimation is 15/63≈ 0.24. The efficiency of pro-posed estimation algorithm (19) is dependent on numberof OFDM symbols in one estimation block. Fig. 12 out-line that withLB=40 the efficiency of proposed algorithmis below 0.3. The efficiency asymptotically approaches to0.24 and reaches the value of conventional comb-type LSestimation withLB=350.

7 CONCLUSION

The PLC channel denotes multipath propagation,strong channel selectivity, attenuation, and environmen-

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tal noise. All those time-variant properties negatively af-fect the data transmission over power line communicationchannel. One of the methods to combat those negativeproperties is to develop adequately estimation algorithmto decrease data transmission errors.

In this paper, the effects of the channel estimationin PLC system using OFDM approach have been stud-ied. One frequency (LS) and one time (LMMSE) domainchannel estimation algorithm have been considered. Alsoone frequency domain based channel estimation algorithmis proposed. The proposed algorithm is combination ofblock- and comb-type pilot arrangement in LS channelestimation. It averages long time channel condition byblock-type estimation and gets real time channel conditionusing comb-type estimation with associated interpolationmethod.

The simulation results bring that proposed LS estima-tion algorithm gives better performance in the form of BERfrom the conventional LS channel estimation algorithm.Also in the case of relatively simple channel complex-ity proposed algorithm shows almost same BER perfor-mance as more complex LMMSE algorithm and stands asgood candidate to substitute complex LMMSE algorithmfor PLC LAN systems for in-home and small office net-work solutions.

References

[1] Hrasnica, H., Haidine, A., Lehnert, R.,Broadband Pow-erline Communications Networks: Network Design. WestSussex, England: John Wiley & Sons, 2004.

[2] Zimmermann, M., Dostert, K., “A multipath model for pow-erline channel,”IEEE Transactions on Communications,vol. 50, no. 4, pp. 553–559, 2002.

[3] Coleri, S., Ergen, M., Puri, A., Ba-Hai, A., “Channel esti-mation techniques based on pilot arrangement in ofdm sys-tems,” IEEE Transactions on Broadcasting, vol. 48, no. 3,pp. 223–229, 2002.

[4] Hsieh, M., Wei, C., “Channel estimation for ofdm systemsbased on comb-type pilot arrangement in frequency se-lective fading channels,”IEEE Transactions on ConsumerElectronics, vol. 44, no. 1, pp. 217–225, 1998.

[5] Tsai, P.Y., Chiueh, T.D., “Frequency-domain interpolation-based channel estimation in pilot-aided ofdm systems,” inIEEE 59th Vehicular Technology Conference, (Milan, Italy),pp. 420–424, MAY 2004.

[6] Khan, S., Salami, A. F., Lawal, W. A. et al., “Characteriza-tion of indoor power lines as data communication channelsexperimental details and results,”World Academy of Sci-ence, Engineering and Technology, vol. 46, pp. 624–629,2008.

[7] M. Babic, M. Hagenau, K. Dostert, J. Bausch, “Theoreticalpostulation of plc channel model,” tech. rep., Open PLCEuropean Research Alliance (OPERA), 2005.

[8] M. Bogdanovic, “Computer based simulation model real-ization of ofdm communication over power lines,” in20thTelecommunications Forum (TELFOR) Proceedings of Pa-pers, (Belgrade, Serbia), pp. 249–252, NOVEMBER 2012.

[9] M. Bogdanovic, S. Rupcic, “Generalized background noisemodeling in power line communication,” in20th Telecom-munications Forum (TELFOR) Proceedings of Papers,(Belgrade, Serbia), pp. 241–244, NOVEMBER 2012.

[10] Y. T. Desta, J. Tao, W. Zhang, “Review on selected chan-nel estimation algorithms for orthogonal frequency divi-sion multiplexing System,”Information Technology Jour-nal, vol. 10, pp. 914–926, 2011.

[11] S. Kay, “A fast and accurate single frequency estimator,”IEEE Transactions on Acoustics, Speech and Signal Pro-cessing, vol. 37, no. 12, pp. 1987–1990, 1987.

[12] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, andP. O. Borjesson, “On channel estimation in ofdm systems,”in IEEE 45th Vehicular Technology Conf., (Chicago, USA),pp. 815–819, JULY 1995.

[13] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson,and P. O. Borjesson, “Ofdm channel estimation by singularvalue decomposition,”IEEE Transactions on Communica-tions, vol. 46, no. 7, pp. 931–939, 1998.

[14] W. Zhou, W. H. Lam, “A fast LMMSE channel estimationmethod for OFDM systems,”EURASIP Journal onWirelessCommunications and Networking, vol. 2009, 2009.

Mario Bogdanovic was born in Osijek, Croatia,in 1978. In 2004 he received the B.Sc. in Electri-cal Engineering (Telecommunications) from theFaculty of Electrical Engineering and Comput-ing, University of Zagreb, Croatia. From 2004 hehas been working at Siemens Convergence Cre-ators (former Siemens) in Zagreb and Osijek asSenior Software Developer. He is now a PhDCandidate in the Faculty of Electrical Engineer-ing and Computing, University of Zagreb. Hismain research interest includes broadband PLC

systems and OFDM channel estimation techniques.

AUTHORS’ ADDRESSES

Mario BogdanovicSiemens Convergence Creators d.o.o.,Županijska 20,31000 Osijek, Croatiaemail: [email protected]

Received: 2013-08-25Accepted: 2014-01-15

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frequency domain based ls channel estimation in ofdm based

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